This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Vibration energy harvesting using macro‑fiber composites

Yang, Yaowen; Tang, Lihua; Li, Hongyun

2009

Yang, Y., Tang, L., & Li, H. (2009). Vibration energy harvesting using macro‑fiber composites.Smart materials and structures, 18(11), 115025‑.

https://hdl.handle.net/10356/99681

https://doi.org/10.1088/0964‑1726/18/11/115025

© 2009 IOP Publishing Ltd. This is the author created version of a work that has been peerreviewed and accepted for publication by Smart Materials and Structures, IOP PublishingLtd. It incorporates referee’s comments but changes resulting from the publishingprocess, such as copyediting, structural formatting, may not be reflected in this document.The published version is available at: [DOI:http://dx.doi.org/10.1088/0964‑1726/18/11/115025].

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1

Vibration Energy Harvesting Using Macro-Fiber Composites

Yaowen YANG 1*, Lihua TANG 2 and Hongyun LI 3

1,2 School of Civil and Environmental Engineering,

Nanyang Technological University,

50 Nanyang Avenue, Singapore 639798

3 Department of Engineering Mechanics,

Shanghai Jiao Tong University,

1954 Huashan Road, Shanghai 200030, P.R.China

1* Corresponding author, cywyang@ntu.edu.sg 2 lihuatang@pmail.ntu.edu.sg

3 hyli@sjtu.edu.cn

2

ABSTRACT

The decreasing energy consumption of today's portable electronics has invoked the

possibility of energy harvesting from ambient environment for self power supply.

One common and simple method for vibration energy harvesting is to utilize the

direct piezoelectric effect. Compared to traditional piezoelectric materials such as

lead zirconate titanate (PZT), macro-fiber composites (MFC) are featured in their

flexibility of large deformation. However, the energy generated by MFC is still far

smaller than that required by electronics at present. In this paper, a vibration energy

harvesting system prototype with MFC patches bonded to a cantilever beam is

fabricated and tested. A finite element analysis (FEA) model is established to

estimate the output voltage of the MFC harvester. The energy accumulation

procedure in the capacitor is simulated by using the electronic design automation

(EDA) software. The simulation results are validated by the experimental ones.

Finally, to optimize the efficiency of energy harvesting, the effects of electrical

properties of MFC as well as the geometric configurations of the cantilever beam

and MFC are parametrically studied by combining the FEA and EDA simulations.

Keywords: energy harvesting; piezoelectric; macro-fiber composite; FEA; EDA.

3

1 INTRODUCTION

With the advancement of integrated circuitry, energy consumption of today’s

electronics continues decreasing, invoking the possibility for micro

electromechanical systems, wireless sensors and portable electronics to harvest

energy from ambient environment for self power supply. There are many energy

sources available in the environment but still not well utilized, such as the vibration

energy. One simple method for vibration energy harvesting is to utilize the direct

piezoelectric effect. Compared to the traditional piezoelectric materials such as lead

zirconate titanate (PZT), the macro-fiber composites (MFC) [1] are featured in

flexibility of large deformation, which enables them to harvest energy from ambient

vibration sources with little brittle risk and long lifespan. However, the current and

energy generated by MFC are still far from fulfilling the consumption requirements

of most portable electronics at present.

In the past few years, many studies have been conducted on the energy generation

ability of piezoelectric materials. Umeda et al [2] investigated the efficiency of a

piezoelectric vibrator which converts the impact vibration energy into the electrical

energy. Ramsey and Clark [3] investigated the feasibility of using a piezoelectric

transducer as power supply for a bio-MEMS application. Since polyvinylidene

fluoride (PVDF) exhibits considerable flexibility compared to PZT, Kymissis et al [4]

developed a parasitic power harvester in shoes to gather energy during walking using

4

PVDF. As a new piezoelectric material, the energy harvesting capability of MFC has

not been fully investigated. Sodano et al [5] compared the efficiencies of three

piezoelectric materials, i.e., the traditional PZT, a quick pack actuator and MFC. It

was concluded that MFC is less efficient compared to the conventional piezoelectric

materials, but how to improve the efficiency of energy harvesting of MFC was not

mentioned. If the efficiency of MFC could be improved, it is expected to be more

applicable than PZT in real applications because of its attractive property of

flexibility.

Improvement of energy harvesting efficiency can be achieved by two ways. The first

way is to improve the power output from the harvester. This can be achieved by

changing the geometric configuration of the system or utilizing multiple pieces or

stack configuration of piezoelectric materials [6, 7]. For a cantilever beam system,

the length, width, thickness, beam shape and free end proof mass can be the

candidate parameters to increase the vibration amplitude and to improve the

strain-induced energy output. Jiang et al [8] modeled a cantilever bimorph with a

proof mass attached to its free end and studied the effect of physical and geometrical

parameters on the performance of power generation. Roundy et al [9] stated that, for

the same volume of PZT, a trapezoidal cantilever could generate more than twice

energy than a rectangular beam.

The second way to improve the efficiency of energy harvesting is to enhance the

5

power extraction ability using optimized energy harvesting circuit. Many researchers

have investigated different energy storage methods and attempted to develop the

optimized circuit for energy extracting. Sodano et al [10] compared the efficiency of

a capacitor and a nickel metal hydride battery as energy storage media. Ottman [11]

developed an adaptive approach for energy harvesting from mechanically excited

piezoelectric element. By using a DC-DC converter with an adaptive control

algorithm, the energy harvested was four times that of direct charging without the

converter. Subsequently, self-adaptive power harvesting circuit using the techniques

termed ‘synchronous electric charge extraction’ [12] and ‘synchronous switch

harvesting on inductor’ [13] has been developed and results showed that the

synchronous circuit was able to increase power transfer by 400%. Yet, the additional

electronics for monitoring and power management on the other hand consumed some

energy harvested. More efficient circuit is still under development.

In this paper, a vibration energy harvesting system prototype with MFC patches on a

cantilever beam is developed. The output voltage of the MFC harvester is

experimentally tested and estimated using the finite element method (FEM).

Subsequently, the procedure of energy storing to the capacitor is simulated using the

electronic design automation (EDA) software. The results are verified with the

experimental ones. By combining the FEM and EDA simulations, parametric

analysis is conducted to evaluate the effects of system parameters for optimal power

harvesting.

6

2 EXPERIMENTAL STUDY

The energy harvesting system is composed of an aluminum cantilever beam, one

piece of P1-type MFC as actuator and two pieces of P2-type MFCs as harvesters, an

energy harvesting circuit EH300A, a small LED bulb and the power supply to the

actuator. The entire system is shown in Fig.1. Note that the P1-type MFC actuator is

used for a good controllable excitation of the system.. It is not needed in the practical

application.

The P1-type MFC utilizes d33 piezoelectric effect (Fig.2) to serve as the actuator to

excite the beam. So the beam vibration amplitude can be tuned by altering the

voltage input to the actuator. The two P2-type MFCs, which utilize the d31 effect

(Fig.2), are attached beside the P1-type MFC, serving as energy harvesters. The

reasons for choosing P1-type MFC as actuator are: (1) d33 is larger than d31; (2) the

operational voltage of P1-type ranges from -500V to +1500V [14], which enables it

suitable for actuation, while the operational voltage of P2-type is only -60V~ +360V;

and (3) the interdigital electrode configuration of P1-type MFC limits the current

output, which is not favorable for energy extraction. Two pieces of P2-type MFC

harvesters are used to test the efficiency of the harvesting system for three cases, i.e.,

one single MFC, two MFCs electrically connected in series and in parallel.

7

For the energy harvesting circuit, we utilize an EH300A module (Fig.3), developed

by Advanced Linear Devices, INC [15]. When an energy source starts to inject

energy into the inputs of the EH300A module in the form of electrical charge

impulses, these charge packets are collected and accumulated in an internal storage

capacitor bank. Fig.4 shows the waveform of voltage across the capacitor bank in

EH300A. Initially, the voltage across the capacitor bank, +V, starts at 0.0V. When

+V reaches VH, the module output (VP) is enabled to supply power to a load. In this

study, the load is an LED bulb. As power is drawn by the LED from the capacitor

bank during time duration t3 (Fig.4), +V decreases. When it reaches VL, output VP

switches off and stops supplying any further power. The charging cycle will restart

until VH is reached again. During each charging cycle that +V increases from VL to

VH or energy is delivered to the load, around 30mJ energy (taken from the datasheet

of EH300A [15]) is accumulated or released. In the experiment, time t2 in Fig.4 for

different cases is our concern since it reflects the efficiency of energy harvesting of

the system. The shorter is it, the higher the efficiency is.

3 FINITE ELEMENT MODELING

To determine the ability of energy generation of MFC, a finite element model is

developed using the commercial code ABAQUS6.6 to calculate the voltage output

from MFC. The geometric configuration is shown in Fig.5. The parameters of

energy harvesting system are list in Table 1. The mesh of finite element model is

8

shown in Fig. 6. The epoxy and aluminum beam are modeled using the reduced

second order solid element, i.e. C3D20R, and the MFC actuator and harvesters are

modeled using the piezoelectric element, i.e. C3D20RE.

3.1 Electrode Modeling

The entire top and bottom surface of P2-type MFC is covered by electrode. In finite

element analysis (FEA), the equation constraint [16] should be imposed on the

electrical potential degrees of the surface nodes to ensure a uniform potential, which

simulates the real electrodes. For the actuator P1-type MFC, it is quite difficult to

directly model the interdigital electrodes. For convenience of analysis, the P1-type

MFC will be equivalently converted to the P2-type MFC so that the top surface and

bottom surface are modeled as electrodes, as shown in Fig. 6. The voltage load on

the P1-type MFC actuator is applied by setting the potential on the bottom electrode

to be zero and imposing the sinusoidal electrical potential on the top electrode. The

equivalent conversion should ensure that the piezoelectric and electrical properties of

the P1-type MFC keep unchanged. For the piezoelectric property, when applying the

same voltage, the strain generated by MFC should be the same:

mm e

VtV

⋅=⋅ 3331 dd’ (1)

where tm=0.25mm and em=0.5mm are the thickness and the distance between two

neighboring interdigital electrodes of P1-type MFC, respectively. Hence, the

equivalent d’31 parameter applied in FEA is calculated as 1.87 E-10 C/N. Besides,

9

the dielectric constant 1.5E-8 F/m before conversion should be changed to 0.3E-8

F/m after conversion such that the capacitance is still 5nF as that of the original

P1-type MFC.

Rayleigh Damping

In FEA, the damping effect should be considered otherwise the calculation would be

terminated because of the convergence problem near the beam resonance. Both

energy extracted from the MFC harvesters and the damping from structure material

contribute to the entire damping effect of the system. However, in FEA, only the

open circuit voltage of MFC harvester is calculated and no energy is removed from

the system, in which case, we assume that the damping of the system is only

attributed to the damping of the beam material. Here, the Rayleigh damping [16] is

considered for the aluminum beam,

⎟⎟⎠

⎞⎜⎜⎝

⎛+= βω

ωαξ i

ii 2

1 (2)

where α and β are the unknown parameters; and iω is the frequency of the ith

vibration mode. To obtain α and β , the damping ratios for the 1st and 2nd

resonance modes should be experimentally determined. Usually, the log decrement

method [17] can be utilized to measure the damping ratio at the resonance frequency,

1

1ln2

1

+⋅=

nAA

nπξ (3)

where A1 and An+1 are the 1st and the (n+1)th peak value of voltage recorded by

10

digital multimeter. A simple experiment has been conducted to record the free

vibration response of the system. Using the experiment data and equation (3), the

damping ratios for the 1st and 2nd modes are obtained as 0.00641 =ξ and

0.00772 =ξ . Applying 1ξ and 2ξ to equation (2), the two parameters of the

Rayleigh damping can be determined as 0.66=α and 5-3.544E=β .

3.3 Results of Steady-State Analysis

Fig.7 shows the strain distribution of the cantilever beam and MFC harvesters at the

1st natural frequency. Figs.8 and 9 show the peak value of strain and RMS voltage

output from one single MFC harvester, respectively. It is noted that the values of

strain and voltage from FEA match well with the experimental results except for

minor shifts on the frequency axis. This could be attributed to the fact that the

cantilever beam is not perfectly clamped, as shown in Fig.1. For the 1st mode, the

natural frequencies obtained from the experiment and simulation results are 9.75Hz

and 10.269Hz, respectively, and the RMS voltage output are 11.5V and 10.8V,

respectively. The differences between the experiment and simulation results are

around 5%. Therefore, the finite element model is able to accurately evaluate the

voltage output of MFC harvester.

In energy harvesting applications with ultra-low frequency (around 1Hz) impulse

input, the cantilever beam will experience free vibration with damping at the 1st

11

natural frequency. At this resonance frequency, the MFC harvester will be subjected

to the maximum strain and hence release the maximum output voltage, as shown in

Fig.9. As a result, the efficiency of energy harvesting at resonance is of great

importance. In later sections, the efficiencies of MFC harvesters are considered at

the 1st natural frequency.

4 ELECTRONIC SIMULATION

The voltage output of MFC harvester can be obtained from FEA. However, based on

these results, we still cannot evaluate the power available to be extracted from the

MFC harvester. Actually, because of the intrinsic capacitance, the power generated

by the MFC harvester will be recovered back to the source. As a result, the

efficiency of energy harvesting system depends on the amount of energy extracted

and stored from the MFC. The EDA software Multisim10.0 by National Instrument

is utilized to simulate the energy extraction and storing procedures from the MFC

harvester. Fig.10 shows the circuit of the energy harvesting system. The EH300A

module is simplified as a full-wave rectifier and a capacitor bank, and the power

management module in EH300A is neglected. As the 1st natural frequency of

cantilever beam is around 10Hz, the impedance from the internal capacitance

(measured 25nF in experiment) is quite large around 637kΩ. The equivalent circuit

[18] of the MFC harvester is composed of a voltage source in series with its internal

capacitance, as shown in the dash box in Fig.10, which is similar to that for the

12

conventional piezoelectric material.

4.1 Efficiency at 1st Natural Frequency

The efficiency of the energy harvesting system at the 1st natural frequency is tested

for 3 cases, namely, one single MFC, two MFCs electrically connected in series and

in parallel. Figs.11 and 12 illustrate the history of charging current to the EH300A

and the energy storing procedure in the capacitor bank of EH300A, respectively.

Again, the simulation results match well with the experimental ones.

Table 2 lists the time t2 (refer to Fig.4) for 30mJ accumulated in EH300A and the

average power of energy storing from the experiment and electronic simulation for

the three cases at the 1st natural frequency. It is noted that MFCs electrically

connected in parallel generate the largest charging current to EH300A and hence are

most efficient to charge the energy storage capacitor with capacitance 6.6mF in

EH300A.

5 OPTIMIZATION OF ENERGY HARVESTING SYSTEM

As shown above, the FEA and EDA simulations are able to accurately evaluate the

voltage output of MFC harvesters and the energy storing to the EH300A. By

combing the two simulations, a parametric analysis can be performed to estimate the

13

optimal power generation of the system. In Table 2, it is noted that the parallel and

series connections alter both the capacitance and the MFC output voltage. The

parallel connection doubles the capacitance of the harvesting system without

changing the voltage output, while the series connection halves the capacitance but

doubles the MFC voltage output. The results of increased average power for energy

storage to EH300A indicate that both the capacitance of MFC harvesters and the

voltage output are the key factors to optimize the efficiency of the energy harvesting

system.

5.1 Effect of MFC Capacitance

The capacitance of MFC can be changed by the dielectric constant, the thickness and

the area of MFC.

Dielectric constant

With the advancement of material science, the dielectric constant of piezoceramics

can be changed during fabrication. Here, 5 values of dielectric constant are

considered to study its effect on the performance of energy harvesting system. On

the contrary to expectation, the dielectric constant fails to show significant influence

on energy harvesting power, as demonstrated in Table 3. This should be attributed to

the accompanying variation of output voltage from the MFC harvester. In Tables 3,

4 and 5, the values with ‘*’ are the actual values of MFC harvester in the

experiment.

14

Thickness of MFC

With decrease in MFC thickness, the capacitance will relatively increase. To our

disappointment, varying the MFC thickness also fails to improve the power

extraction from the MFC, as shown in Table 4.

MFC stack configuration

The fact that changing the dielectric constant or MFC thickness can not improve the

energy harvesting power is probably attributed to that the charges available to be

extracted do not increase or even decrease for the specific MFC area. As for

increasing the area of MFC, multiple MFCs electrically connected in parallel have

been proven the most efficient. But increasing MFC area as in the experiment is not

suitable for a wearable energy harvesting application. Thus, we try another way to

equivalently increase the area of MFC, i.e., using the MFC stack configuration

where multiple MFCs are geometrically connected in series while electrically in

parallel, which is favorable to reduce the size of the energy harvesting system. In

Table 5, it is observed that for the 2-layer MFC stack configuration, the energy

extraction power can achieve a maximum increase of 26% compared to the

non-stack configuration. But for more layers of MFC, the energy extraction power

decreases. This is due to the fact that the multilayer stack configuration limits the

flexibility of MFC, which in turn reduces the beam vibration and hence the output

voltage, as shown in Table 5.

15

5.2 Varying Beam Dimensions

The above results on the variation of MFC capacitance affirm that the MFC voltage

output is another important factor that affects the system performance. In this section,

the beam dimensions will be optimized to increase the beam vibration amplitude.

Besides, the beam dimensions will also affect the 1st natural frequency. Here, only

the thickness and length of the beam are considered for optimization. With larger

thickness and smaller length, higher natural frequency is expected, while with larger

thickness and length, lower voltage output from the MFC harvester is expected, as

shown in Figs.13 and 14.

With the given impedance, higher open circuit voltage means higher current, which

is favorable for charge accumulation in a capacitor or battery. However, besides the

capacitance in the capacitive energy harvesting circuit (Fig.10), the impedance also

depends on the excitation frequency. In this work, we only consider the power

achieved at the 1st natural frequency. The structural configuration for maximum open

circuit voltage does not ensure the maximum power output at the 1st natural

frequency (used as the excitation frequency). The maximum power output is

achieved with the trade-off between the open circuit voltage and the natural

frequency, as shown in Figs.13-15. With 7 values of length and 6 values of

thickness in the simulation, the optimized power can be obtained at length=250mm

and thickness=1.5mm, as shown in Fig.15.

16

5.3 Optimized Energy Harvesting Performance

Based on the above parametric analysis, for optimal energy harvesting performance,

it is recommended to use the 2-layer MFC stack configuration with the beam

dimensions of 250mm×62mm×1.5mm. The energy harvesting power can be

optimized as 151.6 μw when the beam vibrates at the 1st natural frequency, as listed

in Table 6.

6 CONCLUSION

In this paper, an energy harvesting system prototype with MFC patches on a

cantilever beam is developed and the efficiency of energy harvesting is tested. A

finite element model for the system is developed and verified with the experimental

results, showing its capability of accurate evaluation of the voltage output from the

MFC harvesters. Subsequently, the procedure of energy extraction and storing to the

capacitor in EH300A is simulated by using the electronic design automation (EDA)

software. By combining the FEM and EDA simulations, parametric analysis is

conducted to optimize the energy harvesting performance of the system. It is found

that with the MFC stack configuration with 2 layers and the beam dimensions of

250mm×62mm×1.5mm, energy extraction from the MFC harvesters can be

optimized. The optimized power of 151.6 μw is achieved when the beam vibrates at

the 1st natural frequency. It is demonstrated that the combined FEM and EDA

17

simulations are useful tools for evaluating and optimizing the efficiency of MFC

based energy harvesting systems, which are also applicable to other piezoelectric

material based systems.

REFERENCES

[1] Werlink R J, Bryant R G and Manos D (2002), “Macro fiber piezocomposite

actuator poling study”, NASA/TM-2002-211434.

[2] Umeda M, Nakamura K and Ueha S (1996), “Analysis of transformation of

mechanical impact energy to electrical energy using a piezoelectric vibrator”,

Jpn J Appl Phys, vol. 35, pp. 3267-3273.

[3] Ramsey M J and Clark W W (2001), “Piezoelectric energy harvesting for bio

MEMS applications”, Proc. SPIE, vol. 4332, pp. 429-438.

[4] Kymissis J, Kendall D, Paradiso J and Gershenfeld N (1998), “Parasitic power

harvesting in shoes”, Second IEEE International Conference on Wearable

Computing, pp. 132-139.

[5] Sodano H A, Inman D J and Park G (2005), “Comparison of piezoelectric

energy harvesting devices for recharging batteries”, J. Intell. Mater. Syst.

Struct., vol. 16, pp. 799-807.

18

[6] Ng T H and Liao W H (2005), “Sensitivity analysis and energy harvesting for a

self-powered piezoelectric sensor”, J. Intell. Mater. Syst. Struct., vol. 16, pp.

785-797.

[7] Platt S R, Farritor S and Harder H (2005), “On low-frequency electric power

generation with PZT ceramics”, IEEE/ASME Trans. Mechatronics, vol. 10, pp.

240-252.

[8] Jiang S, Li X, Guo S, Hu Y, Yang J and Jiang Q (2005), “Performance of a

piezoelectric bimorph for scavenging vibration energy”, Smart Mater. Struct.,

vol. 14, pp. 769-774.

[9] Roundy S, Leland E S, Baker J, Carleton E, Reilly E, Lai E, Otis B, Rabaey J

M, Wright P K and Sundararajan V (2005), “Improving power output for

vibration-based energy scavengers”, Pervasive Computing, IEEE, vol. 4, pp.

28-36.

[10] Sodano H A, Inman D J and Park G (2005), “Generation and storage of

electricity from power harvesting devices”, J. Intell. Mater. Syst. Struct., vol.

16, pp. 67-75.

[11] Ottman G K (2002), “Adaptive piezoelectric energy harvesting circuit for

wireless remote power supply”, IEEE Trans. on Power Electronics, vol. 17, pp.

669-676.

19

[12] Lefeuvre E, Badel A, Richard C and Guyomar D (2005), “Piezoelectric energy

harvesting device optimization by synchronous electric charge extraction”, J.

Intell. Mater. Syst. Struct., vol. 16, pp. 865-876.

[13] Badel A, Guyomar D, Lefeuvre E and Richard C (2005), “Efficiency

enhancement of a piezoelectric energy harvesting device in pulsed operation by

synchronous charge inversion”, J. Intell. Mater. Syst. Struct., vol. 16, pp.

889-901.

[14] http://www.smart-material.com/MFC/MFC_specs.php

[15] EH300A datasheet, http://www.aldinc.com/pdf/EH300ds.pdf

[16] ABAQUS Analysis User’s Manual, Version 6.6-1, Section 28.2.1: Linear

constraint equations, and Section 20.1.1: Material damping (2006).

[17] Meirovitch L (2005), Fundamentals of Vibrations (New York: McGraw-Hill).

[18] Park C H (2001), “On the circuit model of piezoceramics”, J. Intell. Mater.

Syst. Struct., vol. 12, pp. 515-522.

20

Table 1 Material and geometric parameters of MFC and cantilever beam

Item Value MFC active area dimensions (both P1- and P2-type) 28mm×14mm×0.25mm MFC piezoelectric constant d33 3.74E-10 C/N MFC piezoelectric constant d31 1.7E-10 C/N MFC dielectric constant 1.5E-8 F/m

MFC elastic constants E1 = 30.34GPa, E3 = 15.86GPa, v13=0.31, G13=5.52GPa

MFC density 7500 Kg/m3 Epoxy dimensions 28mm×14mm×0.1mm Epoxy elastic constants E=0.1GPa, v=0.38 Epoxy density 2200 Kg/m3 Aluminum beam dimensions 350mm×62mm×1.5mm Aluminum elastic constants E = 68GPa, v=0.35 Aluminum density 2700 Kg/m3

Table 2 Energy harvesting performance for three cases

Experiment Simulation

MFC connection

Capacitance (nF)

Open circuit

Vrms(V) t2 (sec) Average

power(μw) t2 (sec) Average power(μw)

single 25 11.5 978 30.67 942 31.85 in series 12.5 21.5 845 35.50 835 35.93

in parallel 50 11.85 450 66.67 471 63.69

Table 3 Energy harvesting performance of MFC with various dielectric constants

MFC dielectric constant (F/m)

Open circuit Vrms (V)

Capacitance (nF)

Time for 30mJ accumulated(sec)

Average power(μw)

1.00E-08 15.9466 16.667 860.403 34.87 1.25E-08 12.8666 20.833 889.418 33.73

1.5E-08(*) 10.7967 25 922.260 32.53 1.75E-08 9.2997 29.17 960.776 31.22 2.00E-08 8.16694 33.33 1004.428 29.87

21

Table 4 Energy harvesting performance of MFC with various thicknesses

MFC thickness

(mm)

1st natural freqency

(Hz)

Open circuit Vrms(V)

Capacitance (nF)

Time for 30mJ accumulated(sec)

Average power(μw)

0.1 10.205 5.41591 62.5 1028.865 29.16 0.15 10.227 7.49473 41.67 912.697 32.87 0.2 10.249 9.24628 31.25 905.464 33.13

0.25 (*) 10.269 10.7967 25 922.260 32.53 0.3 10.291 12.1485 20.833 952.331 31.50 0.35 10.311 13.3117 17.857 991.425 30.26

Table 5 Energy harvesting performance of MFC multilayer stack configurations

Multilayer number

1st natural frequency

(Hz)

Open circuit

Vrms(V)

RMS tip deflection

(mm)

Capacitance (nF)

Time for 30mJ accumulated

(sec)

Average power(μw)

1(*) 10.269 10.7967 9.28 25 922.260 32.53 2 10.367 7.62901 8.64 50 732.332 40.97 3 10.436 5.47782 8.18 75 823.795 36.42 4 10.487 4.07801 7.84 100 1142.759 26.25

Table 6 Optimized performance of MFC energy harvesting system

1st natural frequency (Hz)

Open circuit Vrms (V)

Capacitance (nF)

Time for 30mJ accumulated(sec)

Average power(μw)

20.575 12.702 50 197.94 151.6

22

Figure 1 MFC energy harvesting system prototype

(a) (b)

Figure 2 P1- and P2-type MFCs (a) P1-type, (b) P2-type

Figure 3 EH300A

Figure 4 Voltage waveform across the capacitor bank in EH300A (from EH300A

datasheet [15])

23

Figure 5 Geometric configuration of cantilever beam with MFC patches

Figure 6 Finite element model

24

Figure 7 Strain and electrical potential distribution at 1st natural frequency

25

0

50

100

150

200

250

0 20 40 60 80

Frequency(Hz)

peak

val

ue o

f stra

in (μ

)

Experiment FEM

Figure 8 Peak value of strain at centre of top surface of MFC harvester

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80

Frequency(Hz)

Ope

n_C

ircui

t_V

olta

ge_r

ms(

v)

Experiment FEM

Figure 9 RMS voltage output of MFC harvester

26

Figure 10 Circuit of energy harvesting system

27

12.515

17.520

22.525

27.530

32.535

0 3 6 9 12 15 18T(min)

Irms(μA

)

Experiment (single MFC) Simulation (Single MFC)Experiment (2 MFCs in series) Simulation (2 MFCs in series)Experiment (2 MFCs in parallel) Simulation (2 MFCs in parallel)

Figure 11 Charging curves for three cases at the first natural frequency

1.8

2.12.4

2.7

3

3.33.6

3.9

0 3 6 9 12 15 18T(min)

Vol

tage

acr

oss

capa

cito

r(v)

Experiment (single MFC) Simulation (Single MFC)Experiment (2 MFCs in series) Simulation (2 MFCs in series)Experiment (2 MFCs in parallel) Simulation (2 MFCs in parallel)

Figure 12 Energy storing procedure for three cases at the first natural

frequency

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Figure 13 1st natural frequency with various beam dimensions

Figure 14 MFC voltage output with various beam dimensions

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Figure 15 Average power of energy extraction with various beam dimensions